Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables

The Mann‐Whitney (MW) statistic is one of the most recommended two‐sample statistical tests when the assumption of normality fails to hold due to its robustness and fascinating properties especially when small sample sizes are involved. In order to improve the sensitivity of the generally weighted moving average (GWMA) monitoring scheme toward the detection of large shifts, in this paper, a new distribution‐free phase II composite Shewhart‐GWMA (CSG) scheme is proposed using the MW U statistic. The performance of the proposed scheme is investigated using the average run‐length (ARL) and average extra quadratic loss (AEQL) values through extensive simulations. The performance of this newly proposed monitoring scheme is found to be superior when compared to numerous memory‐type MW schemes (some existing and others introduced in this paper) in many situations. An illustrative example is given to demonstrate the implementation of the CSG MW U scheme using real‐life data.

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“…A monitoring scheme is

A R L

‐biased if at time t the

A R L_{1}

value is greater or equal to the attained

A R L_{0}

value, see Tran and Knoth 47 . From Figures 1 and 2, it can be seen that, when q is small, the U‐CSG scheme is

A R L

‐biased under skewed distributions for small phase I and phase II sample sizes.…”

Section: Performance Study Of the Proposed Monitoring Schemementioning

confidence: 98%

Distribution‐free composite Shewhart‐GWMA Mann‐Whitney charts for monitoring the process location

Mabude

Malela‐Majika

Aslam

et al. 2020

Quality & Reliability Eng

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“…Then two separate one-sided EWMA charts were studied by some researchers. For instance, Tran et al [19] and Tran and Knoth [20] studied the properties of two one-sided EWMA charts to monitor the ratio of two variables. Zhang et al [21] and Muhammad et al [22] investigated the performance of two one-sided EWMA charts for monitoring the coefficient of variation (CV).…”

Section: Introductionmentioning

confidence: 99%

Modified One-Sided EWMA Charts without- and with Variable Sampling Intervals for Monitoring a Normal Process

Zhang

Sun

et al. 2022

Symmetry

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Much research has been conducted on two-sided Exponentially Weighted Moving Average (EWMA) control charts, while less work has been devoted to the one-sided EWMA charts. Traditional one-sided EWMA charts involve resetting the EWMA statistic to the target whenever it falls below or above the target, or truncating the observations above or below the target and further applying the EWMA statistic to the truncated samples. In order to further improve the performance of traditional one-sided EWMA mean (X¯) charts, this paper studies the performance of the Modified One-sided EWMA (MOEWMA) X¯ charts to monitor a normally distributed process. The Monte-Carlo simulation method is used to obtain the zero- and steady-state Run Length (RL) properties of the proposed control charts. Through extensive simulations and comparisons with other charts, it is shown that the proposed MOEWMA X¯ charts compare favorably with some existing competing charts. Moreover, by attaching the variable sampling intervals (VSI) feature to the MOEWMA X¯ charts, it is shown that the VSI MOEWMA charts outperform the corresponding charts without the VSI feature. Finally, a real data example from manufacturing process shows the implementation of the proposed one-sided charts.

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“…An assessment of the Shewhart ratio chart's performance when measurement errors are present by considering the linear covariate error model was made by Tran et al 9 . Tran and Knoth 10 advocated an unbiased EWMA ratio scheme for monitoring the ratio of two normal variables. The variable sampling intervals (VSI) EWMA and CUSUM schemes to monitor the ratio of two normal variables were suggested by Nguyen et al 11,12 .…”

Section: Introductionmentioning

confidence: 99%

Run sum ratio chart when measurement errors are present

Abubakar

Khoo

Saha

et al. 2022

Quality & Reliability Eng

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As far as literature of quality control is concerned, this is the first article that advocates the run sum ratio scheme with measurement errors, called the RS‐RZ ME chart. The linear covariate error model is employed in designing the RS‐RZ ME chart in detecting increases and decreases in the ratio of two variables from the normal distribution. The average run length and expected average run length values of the RS‐RZ ME chart are obtained using the Markov chain model. A comparison of the RS‐RZ ME scheme with two measurement errors based charts in the literature, namely, the Shewhart ratio and standard run sum ratio charts is conducted. The results indicate the superiority of the RS‐RZ ME chart over the aforesaid existing charts for most of the shift sizes and shift intervals considered. The findings reveal that as the values of the parameters controlling the accuracy error of the measurement system, false(θX,θYfalse)$({{\theta _X},{\theta _Y}} )$ increase, the RS‐RZ ME scheme's efficiency increases. In the same vein, as the values of the parameters controlling the precision of the measurement system, false(ηX,ηYfalse)$( {{\eta _X},{\eta _Y}} )$ decrease, the RS‐RZ ME scheme’ efficiency increases. Furthermore, as the value of the correlation coefficient between variables X and Y increases, the RS‐RZ ME chart's efficiency increases. The application of the RS‐RZ ME scheme is illustrated using data from a food industry.

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Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables

Cited by 20 publications

References 35 publications

Distribution‐free composite Shewhart‐GWMA Mann‐Whitney charts for monitoring the process location

Distribution‐free composite Shewhart‐GWMA Mann‐Whitney charts for monitoring the process location

Modified One-Sided EWMA Charts without- and with Variable Sampling Intervals for Monitoring a Normal Process

Run sum ratio chart when measurement errors are present

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